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• W2182822453 abstract "The general aim of this talk is to advocate a combinatorial perspective, together with its methods, in the investigation and study of models of computa- tion structures. This, of course, should be taken in conjunction with the well- established views and methods stemming from algebra, category theory, domain theory, logic, type theory, etc. In support of this proposal I will show how such an approach leads to interesting connections between various areas of computer sci- ence and mathematics; concentrating on one such example in some detail. Specif- ically, I will consider the line of my research involving denotational models of the pi calculus and algebraic theories with variable-binding operators, indicating how the abstract mathematical structure underlying these models fits with that of Joyal's combinatorial species of structures. This analysis suggests both the unification and generalisation of models, and in the latter vein I will introduce generalised species of structures and their calculus. These generalised species encompass and generalise various of the notions of species used in combina- torics. Furthermore, they have a rich mathematical structure (akin to models of Girard's linear logic) that can be described purely within Lawvere's generalised logic. Indeed, I will present and treat the cartesian closed structure, the linear structure, the differential structure, etc. of generalised species axiomatically in this mathematical framework. As an upshot, I will observe that the setting allows for interpretations of computational calculi (like the lambda calculus, both typed and untyped; the recently introduced differential lambda calculus of Ehrhard and Regnier; etc.) that can be directly seen as translations into a more basic elemen- tary calculus of interacting agents that compute by communicating and operating upon structured data." @default.
• W2182822453 created "2016-06-24" @default.
• W2182822453 creator A5080675787 @default.
• W2182822453 date "2005-01-01" @default.
• W2182822453 modified "2023-09-27" @default.
• W2182822453 title "Mathematical Models of Computational and Combinatorial Structures (Invited Address)" @default.
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